Package ffx.numerics.special

Class ModifiedBessel

java.lang.Object
ffx.numerics.special.ModifiedBessel
public class ModifiedBessel extends Object
Implementation of the modified Bessel function of the first kind using Chebyshev polynomials.

Adapted from the CERN "cern.jet.math.tdouble" package as included with the ParallelColt library.

  • Method Summary

    Modifier and Type
    Method
    Description
    static double
    i0(double x)
    Modified zero-order Bessel function.
    static double
    i1(double x)
    Modified 1st-order Bessel function.
    static double
    i1OverI0(double x)
    Compute the ratio of i1(x) to i0(x).
    static double
    lnI0(double x)
    Compute the natural log(i0(x)).

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Method Details

    • i0

      public static double i0(double x)
      Modified zero-order Bessel function.

      The function is defined as i0(x) = J0( ix ). The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.

      Parameters:
      x - input parameter
      Returns:
      i0(x)

    • i1

      public static double i1(double x)
      Modified 1st-order Bessel function.

      The function is defined as i1(x) = -i j1( ix ). The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.

      Parameters:
      x - input parameter.
      Returns:
      i1(x).

    • i1OverI0

      public static double i1OverI0(double x)
      Compute the ratio of i1(x) to i0(x).

      This implementation avoids redundant calculations by computing both i1(x) and i0(x) efficiently for different ranges of x.

      Parameters:
      x - input parameter
      Returns:
      i1(x) / i0(x)

    • lnI0

      public static double lnI0(double x)
      Compute the natural log(i0(x)).

      This implementation computes log(i0(x)) directly to avoid overflow for large x values. For large x, i0(x) ~ exp(x)/sqrt(2*pi*x), so log(i0(x)) ~ x - 0.5*log(2*pi*x).

      Parameters:
      x - input parameter.
      Returns:
      the natural log(i0(x)).